SOLUTION: how many different triangles can you make with a perimeter of 12 units?

Question 996435: how many different triangles can you make with a perimeter of 12 units?

Found 2 solutions by Fombitz, rothauserc:
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
An infinite number.
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
If you mean that the sides of the triangle can be real numbers (decimals or fractions), then there are an infinite number of triangles that can be constructed.
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If you mean that the sides of the triangle are whole numbers, then there is a limited number of possible triangles. We are looking for solutions that solve
a + b + c = 12
The triangle inequality says that the sum of any two sides of a triangle must be greater than the third. Therefore, we can write down the possibilities
1) 2 - 5 - 5
2) 3 - 5 - 4
3) 4 - 4 - 4
4) 5 - 4 - 3
5) 5 - 5 - 2
There are 5 possibilities
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